2 citations · 2 across the 5 of their papers we have counts for
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Space-grid approximations of hybrid stochastic differential equations and first passage properties
Hansjoerg Albrecher, Oscar Peralta
Hybrid stochastic differential equations are a useful tool to model continuously varying stochastic systems which are modulated by a random environment that may depend on the syste…
A Markov jump process associated with the matrix-exponential distribution
Oscar Peralta
Let be the density function associated to a matrix-exponential distribution of parameters . By exponentially tilting , we find a probabilistic interpretation which…
RAP-modulated Fluid Processes: First Passages and the Stationary Distribution
Nigel G. Bean, Giang T. Nguyen, Bo F. Nielsen +1
We construct a stochastic fluid process with an underlying piecewise deterministic Markov process (PDMP) akin to the one used in the construction of the rational arrival process (R…
Wong--Zakai approximations with convergence rate for stochastic differential equations with regime switching
Giang T. Nguyen, Oscar Peralta
We construct Wong--Zakai approximations of time--inhomogeneous stochastic differential equations with regime switching (RSSDEs), and provide a convergence rate. %Given a family of…
An explicit solution to the Skorokhod embedding problem for double exponential increments
Giang T. Nguyen, Oscar Peralta
Strong approximations of uniform transport processes to the standard Brownian motion rely on the Skorokhod embedding of random walk with centered double exponential increments. In…
Rate of Strong Convergence to Markov-modulated Brownian motion
Giang T. Nguyen, Oscar Peralta
In Latouche and Nguyen (2015), the authors constructed a sequence of stochastic fluid processes and showed that it converges weakly to a Markov-modulated Brownian motion (MMBM). He…