First-passage probabilities and invariant distributions of Kac-Ornstein-Uhlenbeck processes
N Ratanov - arXiv preprint arXiv:2102.13308, 2021 - arxiv.org
In this paper, we study Ornstein-Uhlenbeck processes with Markov modulation, whose
parameters depend on an external underlying two-state Markov process. Conditional mean …
parameters depend on an external underlying two-state Markov process. Conditional mean …
Markov-modulated ornstein–uhlenbeck processes
In this paper we consider an Ornstein–Uhlenbeck (OU) process (M (t)) t≥ 0 whose
parameters are determined by an external Markov process (X (t)) t≥ 0 on a finite state space …
parameters are determined by an external Markov process (X (t)) t≥ 0 on a finite state space …
Kac-Ornstein-Uhlenbeck processes: stationary distributions and exponential functionals
N Ratanov - Methodology and Computing in Applied Probability, 2022 - Springer
Abstract We study Ornstein-Uhlenbeck processes whose parameters are modulated by an
external two-state Markov process. The conditional means of such a process for a given …
external two-state Markov process. The conditional means of such a process for a given …
Stationary density function for a random evolution driven by a Markov-switching Ornstein–Uhlenbeck process with finite velocity
AA Pogorui, RM Rodríguez-Dagnino - Random Operators and …, 2022 - degruyter.com
In this paper, we consider a new telegraph process of Ornstein–Uhlenbeck type. The
process is obtained by generalizing the telegraph process in a similar manner to how the …
process is obtained by generalizing the telegraph process in a similar manner to how the …
[HTML][HTML] Extremes of q-Ornstein–Uhlenbeck processes
Y Wang - Stochastic Processes and their Applications, 2018 - Elsevier
Two limit theorems are established on the extremes of a family of stationary Markov
processes, known as q-Ornstein–Uhlenbeck processes with q∈(− 1, 1). Both results are …
processes, known as q-Ornstein–Uhlenbeck processes with q∈(− 1, 1). Both results are …
Large jumps of q-Ornstein–Uhlenbeck processes
Y Wang - Statistics & Probability Letters, 2016 - Elsevier
We continue the investigation of sample paths of q-Ornstein–Uhlenbeck processes. We
show that for each q∈(− 1, 1), the process has big jumps crossing from near one end point …
show that for each q∈(− 1, 1), the process has big jumps crossing from near one end point …
Evolution Systems of Measures for Non-autonomous Ornstein-Uhlenbeck Processes with L\'evy noise
R Wooster - arXiv preprint arXiv:0901.2899, 2009 - arxiv.org
arXiv:0901.2899v5 [math.PR] 4 May 2012 Page 1 arXiv:0901.2899v5 [math.PR] 4 May 2012
EVOLUTION SYSTEMS OF MEASURES FOR NON-AUTONOMOUS ORNSTEIN-UHLENBECK …
EVOLUTION SYSTEMS OF MEASURES FOR NON-AUTONOMOUS ORNSTEIN-UHLENBECK …
Martingales and First-Passage Times for Ornstein--Uhlenbeck Processes with a Jump Component
A Novikov - Theory of Probability & Its Applications, 2004 - SIAM
Using martingale technique, we show that a distribution of the first-passage time over a level
for the Ornstein--Uhlenbeck process with jumps is exponentially bounded. In the case of …
for the Ornstein--Uhlenbeck process with jumps is exponentially bounded. In the case of …
On stationary Markov processes with polynomial conditional moments
PJ Szabłowski - arXiv preprint arXiv:1312.4887, 2013 - arxiv.org
We study a class of stationary Markov processes with marginal distributions identifiable by
moments such that every conditional moment of degree say $ m $ is a polynomial of degree …
moments such that every conditional moment of degree say $ m $ is a polynomial of degree …
Long time behavior of diffusions with Markov switching
JB Bardet, H Guérin, F Malrieu - arXiv preprint arXiv:0912.3231, 2009 - arxiv.org
Let $ Y $ be an Ornstein-Uhlenbeck diffusion governed by an ergodic finite state Markov
process $ X $: $ dY_t=-\lambda (X_t) Y_tdt+\sigma (X_t) dB_t $, $ Y_0 $ given. Under …
process $ X $: $ dY_t=-\lambda (X_t) Y_tdt+\sigma (X_t) dB_t $, $ Y_0 $ given. Under …