scholarly journals The hitting characteristics of a strong Markov process, with applications to continuous martingales in $R^n$

1966 ◽  
Vol 72 (6) ◽  
pp. 1026-1028
Author(s):  
G. E. Denzel
Keyword(s):  
Markov Process ◽  
Strong Markov Process ◽  
Strong Markov

scholarly journals Excision of a strong Markov process

1972 ◽  
Vol 23 (2) ◽  
pp. 114-120 ◽  
Author(s):  
F. B. Knight ◽  
A. O. Pittenger
Keyword(s):  
Markov Process ◽  
Strong Markov Process ◽  
Strong Markov

scholarly journals Parametrix construction for certain Lévy-type processes

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Victoria Knopova ◽  
Alexei Kulik
Keyword(s):  
Markov Process ◽  
Probability Density ◽  
Lower Bounds ◽  
Transition Probability ◽  
Local Operator ◽  
Upper And Lower Bounds ◽  
Transition Probability Density ◽  
Strong Markov Process ◽  
Non Local ◽  
Strong Markov

AbstractIn this paper, we show that a non-local operator of certain type extends to the generator of a strong Markov process, admitting the transition probability density. For this transition probability density we construct the intrinsic upper and lower bounds, and prove some smoothness properties. Some examples are provided.

scholarly journals Quasi-Regular Dirichlet Forms: Examples and Counterexamples

1995 ◽  
Vol 47 (1) ◽  
pp. 165-200 ◽  
Author(s):  
Michael Röckner ◽  
Byron Schmuland
Keyword(s):  
Markov Process ◽  
Dirichlet Forms ◽  
Loop Spaces ◽  
Strong Markov Process ◽  
Speed Measure ◽  
Strong Markov

AbstractWe prove some new results on quasi-regular Dirichlet forms. These include results on perturbations of Dirichlet forms, change of speed measure, and tightness. The tightness implies the existence of an associated right continuous strong Markov process. We also discuss applications to a number of examples including cases with possibly degenerate (sub)-elliptic part, diffusions on loop spaces, and certain Fleming- Viot processes.

Two extreme value processes arising in hydrology

1976 ◽  
Vol 13 (1) ◽  
pp. 190-194 ◽  
Author(s):  
Alan F. Karr
Keyword(s):  
Markov Process ◽  
Random Measure ◽  
Extreme Value ◽  
Poisson Random Measure ◽  
One Dimensional ◽  
Flood Peak ◽  
Base Level ◽  
Strong Markov Process ◽  
Hydrological System ◽  
Strong Markov

Let Tn be the time of occurrence of the nth flood peak in a hydrological system and Xn the amount by which the peak exceeds a base level. We assume that ((Tn, Xn)) is a Poisson random measure with mean measure μ(dx) K(x, dy). In this note we characterize two extreme value processes which are functionals of ((Tn, Xn)). The set-parameterized process {MA} defined by MA = sup {Xn:Tn ∈ A} is additive and we compute its one-dimensional distributions explicitly. The process (Mt), where Mt = sup{Xn: Tn ≦ t}, is a non-homogeneous strong Markov process. Our results extend but computationally simplify those of previous models.

Two extreme value processes arising in hydrology

1976 ◽  
Vol 13 (01) ◽  
pp. 190-194 ◽  
Author(s):  
Alan F. Karr
Keyword(s):  
Markov Process ◽  
Random Measure ◽  
Extreme Value ◽  
Poisson Random Measure ◽  
One Dimensional ◽  
Flood Peak ◽  
Base Level ◽  
Strong Markov Process ◽  
Hydrological System ◽  
Strong Markov

Let Tn be the time of occurrence of the nth flood peak in a hydrological system and Xn the amount by which the peak exceeds a base level. We assume that ((Tn , Xn )) is a Poisson random measure with mean measure μ(dx) K(x, dy). In this note we characterize two extreme value processes which are functionals of ((Tn , Xn )). The set-parameterized process {MA } defined by MA = sup {Xn :Tn ∈ A} is additive and we compute its one-dimensional distributions explicitly. The process (Mt ), where Mt = sup{Xn : Tn ≦ t}, is a non-homogeneous strong Markov process. Our results extend but computationally simplify those of previous models.

The Proof of Strong Markov Property Based on one Definition

2015 ◽  
Vol 742 ◽  
pp. 419-428
Author(s):  
Rong Tang ◽  
Yi Xuan Dong
Keyword(s):  
Markov Process ◽  
Markov Property ◽  
Subject Classification ◽  
Strong Markov Property ◽  
Homogeneous Markov Process ◽  
Primary 60J25 ◽  
Strong Markov Process ◽  
2000 Mathematics Subject Classification ◽  
Strong Markov

In this paper, for countable homogeneous Markov process, we prove strong Markov property defining by [2] are valid. So for an arbitrary countable homogeneous Markov process is a strong Markov process.2000 Mathematics Subject Classification. Primary 60J25, 60J27.

Coincident probabilities and applications in combinatorics

1988 ◽  
Vol 25 (A) ◽  
pp. 185-200 ◽  
Author(s):  
Samuel Karlin
Keyword(s):  
Markov Process ◽  
Individual Component ◽  
Combinatorial Problems ◽  
Particle Systems ◽  
Determinant Formula ◽  
Component Processes ◽  
The Individual ◽  
Multiple Particle ◽  
Inhomogeneous Random Walks ◽  
Strong Markov

For a strong Markov process on the line with continuous paths the Karlin–McGregor determinant formula of coincidence probabilities for multiple particle systems is extended to allow the individual component processes to start at variable times and run for variable durations. The extended formula is applied to a variety of combinatorial problems including counts of non-crossing paths in the plane with variable start and end points, dominance orderings, numbers of dominated majorization orderings, and time-inhomogeneous random walks.

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