A Matching Theorem for Locally Stationary Random Processes
A Matching Theorem for Locally Stationary Random Processes
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E. Second order) properties of random processes.
2 - of x(t), since it can be estimated frcan a knowledge of x(t) in any suf- ficiently large interval.
For the considerations that follow, it is important to impose some regularity conditions on p(t, t'). The most natural requirements, both from a mathematical and physical point of view, are the following: 1. Ctontinulty condition . We assume that (""(tjf) is continuous for all t, t'. As is well known, continxilty of [""(t^f) everywhere is implie...d by continuity of P(t, t*) on the line t=^\ and is equivalent to mean square continuity of x(t) (see [5], p.^YO). It is easy to see that continuity of r'(t, t') is equivalent to continuity of P, (t) and P (t).
2. Integrability conditions . We assume that both I P-(T)d'r and I I Pp('t)|drare finite, * which implies (but is not implied by) the exis- tence of I P(t, t') |dtdt' . This condition corresponds to the physically reasonable assimiption that both the average total energy and the memory of the process be finite (where I | Pp(T)|d'r is used as a measure of memory).
What to read after A Matching Theorem for Locally Stationary Random Processes?
You can find similar books in the "Read Also" column, or choose other free books by Richard a Silverman to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
E. Second order) properties of random processes.
2 - of x(t), since it can be estimated frcan a knowledge of x(t) in any suf- ficiently large interval.
For the considerations that follow, it is important to impose some regularity conditions on p(t, t'). The most natural requirements, both from a mathematical and physical point of view, are the following: 1. Ctontinulty condition . We assume that (""(tjf) is continuous for all t, t'. As is well known, continxilty of [""(t^f) everywhere is implie...d by continuity of P(t, t*) on the line t=^\ and is equivalent to mean square continuity of x(t) (see [5], p.^YO). It is easy to see that continuity of r'(t, t') is equivalent to continuity of P, (t) and P (t).
2. Integrability conditions . We assume that both I P-(T)d'r and I I Pp('t)|drare finite, * which implies (but is not implied by) the exis- tence of I P(t, t') |dtdt' . This condition corresponds to the physically reasonable assimiption that both the average total energy and the memory of the process be finite (where I | Pp(T)|d'r is used as a measure of memory).
What to read after A Matching Theorem for Locally Stationary Random Processes?
You can find similar books in the "Read Also" column, or choose other free books by Richard a Silverman to read onlineMoreLess
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