Feller minimal transition functions, monotone transition functions, Feller–Reuter–Riley transition functions, Feller–Reuter–Riley q-matrices, ordinary ergodicity, strong ergodicity, zero-entrance

Zhang, Hanjun, Chen, Anyue, Lin, Xiang and Hou, Zhenting (2001) Strong ergodicity of monotone transition functions. Statistics & Probability Letters, 55 (1). pp. 63-69. ISSN 0167-7152 (doi:https://doi.org/10.1016/S0167-7152(01)00130-4)

Feller–Reuter–Riley functions, stable q-matrix, unstable q-matrix, Markov branching process, dual, Feller minimal q-functions, Williams-matrix

Chen, Anyue (2001) Applications of Feller-Reuter-Riley transition functions. Journal of Mathematical Analysis and Applications, 260 (2). pp. 439-456. ISSN 0022-247X (doi:https://doi.org/10.1006/jmaa.2000.7466)

Generalized Markov Branching Processes, GMBP, probability

Chen, Anyue (2002) Generalized Markov branching processes. In: International Congress of Mathematicians (ICM2002), 20-28 Aug 2002, Beijing, China.

Markov branching process, weighted Markov branching process, regularity and uniqueness, extinction, explosion

Chen, Anyue, Li, Junping and Ramesh, N.I. ORCID: 0000-0001-6373-2557 (2005) Uniqueness and extinction of weighted Markov branching processes. Methodology and Computing in Applied Probability, 7 (4). pp. 489-516. ISSN 1387-5841 (Print), 1573-7713 (Online) (doi:https://doi.org/10.1007/s11009-005-5005-y)

Markov branching processes (MBP), generalised Markov branching processes (GMBP), uniqueness, differential–integral equation, extinction probability, mean extinction time, conditional mean extinction time

Chen, Anyue (2002) Uniqueness and extinction properties of generalised Markov branching processes. Journal of Mathematical Analysis and Applications, 274 (2). pp. 482-494. ISSN 0022-247X (doi:https://doi.org/10.1016/S0022-247X(02)00251-2)

algebra, analysis, applications of mathematics, mathematical and computational physics

Liu, Kai and Chen, Anyue (2001) A class of generalized Lévy Laplacians in infinite dimensional calculus. Israel Journal of Mathematics, 124 (1). pp. 157-176. ISSN 0021-2172

annihilation, birth-death process, catastrophe, equilibrium distribution, factorial moments, mass immigration, occupation probabilities, resolvent, uniqueness

Renshaw, Eric and Chen, Anyue (1997) Birth-death processes with mass annihilation and state-dependent immigration. Communications in Statistics. Stochastic Models, 13 (2). pp. 239-253. ISSN 0882-0287 (doi:https://doi.org/10.1080/15326349708807424)

annihilation, catastrophe, equilibrium distribution, existence, Markov branching process, q-matrix, recurrence, resolvent, state-dependent immigration

Chen, Anyue and Renshaw, Eric (2000) Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration. Stochastic Processes and their Applications, 88 (2). pp. 177-193. ISSN 0304-4149 (doi:https://doi.org/10.1016/S0304-4149(99)00125-8)

birth-death process, disaster, instantaneous resurrection, unstable continuous-time Markov chain, existence, uniqueness, recurrence, ergodicity, equilibrium distribution, symmetry, reversibility

Chen, Anyue, Zhang, Hanjun, Liu, Kai and Rennolls, Keith (2004) Birth-death processes with disaster and instantaneous resurrection. Advances in Applied Probability, 36 (1). pp. 267-292. ISSN 0001-8678 (doi:https://doi.org/10.1239/aap/1077134473)

birth-death process, unstable continuous-time Markov chain, existence, uniqueness, ergodicity, equilibrium distribution

Chen, Anyue and Liu, Kai (2003) Birth-death processes with an instantaneous reflection barrier. Journal of Applied Probability, 40 (1). pp. 163-179. ISSN 0021-9002 (doi:https://doi.org/10.1239/jap/1044476833)

bulk arrival, busy period distribution, equilibrium distribution, idle time, queue size, recurrence, state-dependent input, waiting-time distribution

Chen, Anyue and Renshaw, Eric (2004) Markovian bulk-arriving queues with state-dependent control at idle time. Advances in Applied Probability, 36 (2). pp. 499-524. ISSN 1475-6064 (Print), 0001-8678 (Online) (doi:https://doi.org/10.1239/aap/1086957583)

continuous-time Markov chains, monotone Q-processes, duality, Feller-Renter-Riley functions, dual q-matrix, Feller q-matrix, conservative, existence, uniqueness, construction

Chen, Anyue and Zhang, Hanjun (1999) Existence, uniqueness and constructions for stochastically monotone Q-processes. Southeast Asian Bulletin of Mathematics, 23 (4). pp. 559-583. ISSN 0129-2021 (Print), 0219-175X (Online)

mathematics

Chen, Anyue, Zhang, Hanjun and Hou, Zhenting (2002) Feller transition functions, Resolvent Decomposition Theorems, and their application in unstable denumerable Markov processes. In: Hou, Zhenting, Filar, Jerzy A. and Chen, Anyue, (eds.) Markov Processes and Controlled Markov Chains. Kluwer Academic Publishers, pp. 15-39. ISBN 9781461379683

Chen, Anyue (1999) Non-linear branching processes. In: International Workshop on Markov Processes & Controlled Markov Chains, 22-28 Aug 1999, Changsha, Hunan, China. (Unpublished)

Chen, Anyue and Renshaw, Eric (1997) The M/M/1 queue with mass exodus and mass arrivals when empty. Journal of Applied Probability, 34 (1). pp. 192-207. ISSN 0021-9002

ordinary ergodicity, strong ergodicity, equilibrium distribution, Markov branching processes, generalised Markov branching processes with resurrection

Chen, Anyue (2002) Ergodicity and stability of generalised Markov branching processes with resurrection. Journal of Applied Probability, 39 (4). pp. 786-803. ISSN 0021-9002 (doi:https://doi.org/10.1239/jap/1037816019)

pollution exposure, pollution, roads, asthma

Rennolls, Keith, Zhang, Yong, Ramesh, Nadarajah ORCID: 0000-0001-6373-2557 , Chen, Anyue and Patel, Swatee (1998) Spatial models of pollution exposure from a road network: the effect on asthma. In: Barnett, Vic, Stein, Albert and Turkman, K. Feridun, (eds.) Statistical Aspects of Health and the Environment. Statistics for the Environment (4). Wiley-Blackwell, Chichester, UK, pp. 137-150. ISBN 9780471976455

regularity, extinction probability, hitting time

Chen, Anyue, Pollett, Phil, Zhang, Hanjun and Li, Junping (2004) The collision branching process. Journal of Applied Probability, 41 (4). pp. 1033-1048. ISSN 0021-9002 (Print), 1475-6072 (Online) (doi:https://doi.org/10.1239/jap/1101840549)

stochastic comparability, duality, stochastic monotonicity, Feller–Reuter–Riley transition functions, zero-exit, zero-entrance

Zhang, Hanjun and Chen, Anyue (1999) Stochastic comparability and dual q-functions. Journal of Mathematical Analysis and Applications, 234 (2). pp. 482-499. ISSN 0022-247X (doi:https://doi.org/10.1006/jmaa.1999.6356)

stochastic differential equations

Liu, Kai and Chen, Anyue (2001) Moment decay rates of solutions of stochastic differential equations. Tohoku Mathematical Journal, 53 (1). pp. 81-93. ISSN 0040-8735

Liu, Kai and Chen, Anyue (2000) An improved result of exponential stability of stochastic semilinear evolution equations. International Journal of Differential Equations and Applications, 1 (1). pp. 99-112. ISSN 1311-2872 (doi:https://doi.org/10.12732/ijdea.vlil.211)

stochastic monotonicity, duality, continuous time Markov chains, non-conservative q -matrix, existence, uniqueness, construction

Chen, Anyue and Zhang, Hanjun (1999) Stochastic monotonicity and duality for continuous time Markov chains with general q-Matrix. Southeast Asian Bulletin of Mathematics, 23. pp. 383-408. ISSN 0129-2021 (Print), 0219-175X (Online)

uniqueness criteria, Markov chains

Chen, Anyue, Pollett, Phil, Zhang, Hanjun and Cairns, Ben (2005) Uniqueness criteria for continuous-time Markov chains with general transition structures. Advances in Applied Probability, 37 (4). pp. 1056-1074. ISSN 0001-8678 (Print), 1475-6064 (Online) (doi:https://doi.org/10.1239/aap/1134587753)