scholarly journals Lévy–Ornstein–Uhlenbeck transition semigroup as second quantized operator

2011 ◽  
Vol 260 (12) ◽  
pp. 3457-3473 ◽  
Author(s):  
S. Peszat
Keyword(s):  
Transition Semigroup

Transition Semigroup

2016 ◽  
pp. 167-195
Author(s):  
Viorel Barbu ◽  
Giuseppe Da Prato ◽  
Michael Röckner
Keyword(s):  
Transition Semigroup

Birth and death on a Brownian flow: a Feller semigroup and its generator and a martingale problem

1996 ◽  
Vol 33 (01) ◽  
pp. 71-87 ◽  
Author(s):  
Michael J. Phelan
Keyword(s):  
Markov Process ◽  
Spatial Configuration ◽  
Martingale Problem ◽  
Stochastic Flow ◽  
Transition Semigroup ◽  
Feller Semigroup ◽  
System Of Particles ◽  
Particle Process

We consider a system of particles in birth and death on a stochastic flow. The system includes a particle process tracking the spatial configuration of live particles on the flow. The particle process is a Markov process on the space of bounded counting measures. We show that its transition semigroup is a Feller semigroup and exhibit its pregenerator. The pregenerator defines a martingale problem. We show that the particle process solves the problem uniquely.

Order continuity of the transition semigroup in Banach spaces

2004 ◽  
Vol 82 (6) ◽  
Author(s):  
M. Abouabassi ◽  
A. Driouich ◽  
O. El-Mennaoui
Keyword(s):  
Banach Spaces ◽  
Transition Semigroup ◽  
Order Continuity

scholarly journals Cores of Potential Operators for Processes With Stationary Independent Increments

1972 ◽  
Vol 48 ◽  
pp. 129-145
Author(s):  
Ken-Iti Sato
Keyword(s):  
Banach Space ◽  
Stochastic Process ◽  
Euclidean Space ◽  
Continuous Functions ◽  
Dimensional Euclidean Space ◽  
Semigroup Of Operators ◽  
Transition Semigroup ◽  
Potential Operators ◽  
Independent Increments

Let Xt(ω)) be a stochastic process with stationary independent increments on the N-dimensional Euclidean space RN, right continuous in t ≧ 0 and starting at the origin. Let C0(RN) be the Banach space of real-valued continuous functions on RN vanishing at infinity with norm . The process induces a transition semigroup of operators Tt on C0(RN) :Ttf(x) = Ef(x + Xt).

Necessary and sufficient conditions for ergodicity of CIR type SDEs with Markov switching

2019 ◽  
Vol 19 (03) ◽  
pp. 1950023 ◽  
Author(s):  
Zhenzhong Zhang ◽  
Hongqian Yang ◽  
Jinying Tong ◽  
Liangjian Hu
Keyword(s):  
Interest Rate ◽  
Markov Switching ◽  
Sufficient Conditions ◽  
Wasserstein Distance ◽  
Necessary And Sufficient Conditions ◽  
Exponential Rate ◽  
Transition Semigroup ◽  
Rate Model ◽  
Interest Rate Model ◽  
Necessary And Sufficient

In this paper, we consider the ergodicity and transience of the Cox–Ingersoll–Ross (CIR) interest rate model with Markov switching. Using the theory of [Formula: see text]-matrices, we give some necessary and sufficient conditions for ergodicity of the CIR interest rate model with Markov switching. Besides, we show that the transition semigroup converges to the stationary distribution at an exponential rate in the Wasserstein distance. Finally, two examples are presented to illustrate our theory.

scholarly journals ANALYSIS OF THE STOCHASTIC FITZHUGH–NAGUMO SYSTEM

2008 ◽  
Vol 11 (03) ◽  
pp. 427-446 ◽  
Author(s):  
STEFANO BONACCORSI ◽  
ELISA MASTROGIACOMO
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Stochastic Differential Equations ◽  
Continuous Dependence ◽  
Infinitesimal Generator ◽  
Ergodic Measure ◽  
Transition Semigroup ◽  
Dissipative Nonlinearity ◽  
Invariant Ergodic Measure

In this paper we study a system of stochastic differential equations with dissipative nonlinearity which arise in certain neurobiology models. Besides proving existence, uniqueness and continuous dependence on the initial datum, we shall mainly be concerned with the asymptotic behaviour of the solution. We prove the existence of an invariant ergodic measure ν associated with the transition semigroup Pt; further, we identify its infinitesimal generator in the space L2 (H; ν).

Exponential ergodicity of CIR interest rate model with random switching

2016 ◽  
Vol 17 (05) ◽  
pp. 1750037 ◽  
Author(s):  
Jinying Tong ◽  
Zhenzhong Zhang
Keyword(s):  
Interest Rate ◽  
Stationary Distribution ◽  
Wasserstein Distance ◽  
Transition Semigroup ◽  
Rate Model ◽  
Cir Model ◽  
Exponential Ergodicity ◽  
The Central Limit Theorem ◽  
Random Switching ◽  
Interest Rate Model

In this paper, we consider ergodicity of Cox–Ingersoll–Ross (CIR) interest rate model with random switching. First, we show that the CIR model with switching has a unique stationary distribution. Next, we prove that the transition semigroup for the CIR model with switching converges to the stationary distribution at an exponential rate in the Wasserstein distance. Moreover, under two particular cases, the explicit expressions for stationary distributions are presented. Finally, the central limit theorem for the CIR model with random switching is established.

Birth and death on a Brownian flow: a Feller semigroup and its generator and a martingale problem

1996 ◽  
Vol 33 (1) ◽  
pp. 71-87 ◽  
Author(s):  
Michael J. Phelan
Keyword(s):  
Markov Process ◽  
Spatial Configuration ◽  
Martingale Problem ◽  
Stochastic Flow ◽  
Transition Semigroup ◽  
Feller Semigroup ◽  
System Of Particles ◽  
Particle Process

We consider a system of particles in birth and death on a stochastic flow. The system includes a particle process tracking the spatial configuration of live particles on the flow. The particle process is a Markov process on the space of bounded counting measures. We show that its transition semigroup is a Feller semigroup and exhibit its pregenerator. The pregenerator defines a martingale problem. We show that the particle process solves the problem uniquely.

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