Ad
related to: stochastic ordering formula example questions worksheet printable 1 2
Search results
Results From The WOW.Com Content Network
Stochastic dominance relations are a family of stochastic orderings used in decision theory: [1] Zeroth-order stochastic dominance: A ≺ ( 0 ) B {\displaystyle A\prec _{(0)}B} if and only if A ≤ B {\displaystyle A\leq B} for all realizations of these random variables and A < B {\displaystyle A<B} for at least one realization.
Malliavin introduced Malliavin calculus to provide a stochastic proof that Hörmander's condition implies the existence of a density for the solution of a stochastic differential equation; Hörmander's original proof was based on the theory of partial differential equations. His calculus enabled Malliavin to prove regularity bounds for the ...
A key example of an optimal stopping problem is the secretary problem. Optimal stopping problems can often be written in the form of a Bellman equation , and are therefore often solved using dynamic programming .
Girsanov's theorem is important in the general theory of stochastic processes since it enables the key result that if Q is a measure that is absolutely continuous with respect to P then every P-semimartingale is a Q-semimartingale.
In the theory of probability for stochastic processes, the reflection principle for a Wiener process states that if the path of a Wiener process f(t) reaches a value f(s) = a at time t = s, then the subsequent path after time s has the same distribution as the reflection of the subsequent path about the value a. [1]
A σ-algebra defines the set of events that can be measured, which in a probability context is equivalent to events that can be discriminated, or "questions that can be answered at time ". Therefore, a filtration is often used to represent the change in the set of events that can be measured, through gain or loss of information .
A common example of a first-hitting-time model is a ruin problem, such as Gambler's ruin. In this example, an entity (often described as a gambler or an insurance company) has an amount of money which varies randomly with time, possibly with some drift. The model considers the event that the amount of money reaches 0, representing bankruptcy.
In the study of stochastic processes in mathematics, a hitting time (or first hit time) is the first time at which a given process "hits" a given subset of the state space. Exit times and return times are also examples of hitting times.