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.

scholarly journals ABSOLUTELY CONTINUOUS COMPENSATORS

2011 ◽  
Vol 14 (03) ◽  
pp. 335-351 ◽  
Author(s):  
SVANTE JANSON ◽  
SOKHNA M'BAYE ◽  
PHILIP PROTTER
Keyword(s):  
Differential Equation ◽  
Markov Process ◽  
Stochastic Differential Equation ◽  
Markov Processes ◽  
Sufficient Conditions ◽  
Random Measure ◽  
Stopping Times ◽  
Poisson Random Measure ◽  
Absolutely Continuous ◽  
Strong Markov

We give sufficient conditions on the underlying filtration such that all totally inaccessible stopping times have compensators which are absolutely continuous. If a semimartingale, strong Markov process X has a representation as a solution of a stochastic differential equation driven by a Wiener process, Lebesgue measure, and a Poisson random measure, then all compensators of totally inaccessible stopping times are absolutely continuous with respect to the minimal filtration generated by X. However Çinlar and Jacod have shown that all semimartingale strong Markov processes, up to a change of time and slightly of space, have such a representation.

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 BSDEs with Logarithmic Growth Driven by Brownian Motion and Poisson Random Measure and Connection to Stochastic Control Problem

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Khalid Oufdil
Keyword(s):  
Optimal Control ◽  
Brownian Motion ◽  
Control Problem ◽  
Stochastic Optimal Control ◽  
Random Measure ◽  
Poisson Random Measure ◽  
One Dimensional ◽  
Stochastic Optimal Control Problem ◽  
Uniqueness Of The Solution ◽  
Logarithmic Growth

Abstract In this paper, we study one-dimensional backward stochastic differential equations under logarithmic growth in the 𝑧-variable ( | z | ⁢ | ln ⁡ | z | | ) (\lvert z\rvert\sqrt{\lvert\ln\lvert z\rvert\rvert}) . We show the existence and the uniqueness of the solution when the noise is driven by a Brownian motion and an independent Poisson random measure. In addition, we highlight the connection of such BSDEs with stochastic optimal control problem, where we show the existence of an optimal strategy for the control problem.

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.

Stability of one-dimensional systems of colliding particles

1976 ◽  
Vol 13 (1) ◽  
pp. 155-158
Author(s):  
Alan F. Karr
Keyword(s):  
Initial Velocity ◽  
Initial Conditions ◽  
Random Measure ◽  
Initial Position ◽  
Dimensional System ◽  
Poisson Random Measure ◽  
Initial Particle ◽  
One Dimensional ◽  
Stability Theorems ◽  
Particle Paths

Envision a one-dimensional system of infinitely many identical particles, in which initial particle positions constitute a Poisson random measure and the initial velocity of a particle depends only on its initial position. Given its initial conditions the system evolves deterministically, by means of perfectly elastic collisions. In this note we derive conditions for continuity of the probability laws of the system and of the particle paths, as functions of the parameters of the initial conditions. These results have the physical interpretation of stability theorems.

Stability of one-dimensional systems of colliding particles

1976 ◽  
Vol 13 (01) ◽  
pp. 155-158
Author(s):  
Alan F. Karr
Keyword(s):  
Initial Velocity ◽  
Initial Conditions ◽  
Random Measure ◽  
Initial Position ◽  
Dimensional System ◽  
Poisson Random Measure ◽  
Initial Particle ◽  
One Dimensional ◽  
Stability Theorems ◽  
Particle Paths

Envision a one-dimensional system of infinitely many identical particles, in which initial particle positions constitute a Poisson random measure and the initial velocity of a particle depends only on its initial position. Given its initial conditions the system evolves deterministically, by means of perfectly elastic collisions. In this note we derive conditions for continuity of the probability laws of the system and of the particle paths, as functions of the parameters of the initial conditions. These results have the physical interpretation of stability theorems.

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.

Sign in / Sign up

Export Citation Format

Share Document