Entrance Time Research Articles

Markov processes with identical hitting probabilities

Let ( X ( t ) , P x ) (X(t),{P^x}) and ( Y ( t ) , Q x ) (Y(t),{Q^x}) be transient Hunt processes on a state space E E satisfying the hypothesis of absolute continuity (Meyer’s hypothesis (L)). Let T ( K ) T(K) be the first entrance time into a set K K , and assume P x ( T ( K ) > ∞ ) = Q x ( T ( K ) > ∞ ) {P^x}(T(K) > \infty ) = {Q^x}(T(K) > \infty ) for all compact sets K ⊆ E K \subseteq E . There exists a strictly increasing continuous additive functional of X ( t ) , A ( t ) X(t),A(t) , so that if T ( t ) = inf { s : A ( s ) > t } T(t) = {\text {inf}}\{s:A(s) > t\} , then ( X ( T ( t ) ) , P x ) (X(T(t)),{P^x}) and ( Y ( t ) , Q x ) (Y(t),{Q^x}) have the same joint distributions. An analogous result is stated if X X and Y Y are right processes (with an additional hypothesis). These theorems generalize the Blumenthal-Getoor-McKean Theorem and have interpretations in terms of potential theory.

A two-person zero-sum Markov game with a stopped set

We consider a two-person zero-sum Markov game with continuous time up to the time that the game process goes into a fixed subset of a countable state space, this subset is called a stopped set of the game. We show that such a game with a discount factor has optimal value function and both players will have their optimal stationary strategies. The same result is proved for the case of a nondiscounted Markov game under some additional conditions, that is a reward rate function is nonnegative and the first time τ (entrance time) of the game process going to the stopped set is finite with probability one (i.e., p( τ < ∞) = 1). It is remarkable that in the case of a nondiscounted Markov game, if the expectation of the entrance time is bounded, and the reward rate function need not be nonnegative, then the same result holds.

RNA polymerase-dependent mechanism for the stepwise T7 phage DNA transport from the virion into E. coli.

The influence of rifampicin, streptolydigin, tetracycline and chloramphenicol on phage DNA transport from the T7 virion into the E. coli cell was studied. It has been found that the DNA transport proceeds in at least three stages. During the initial stage the phage injects into the host cell the left approximately 10 per cent of its DNA molecule. The entrance of the next 50 per cent of 17 DNA molecule is blocked by inhibitors which block transcription but not translation. Moreover, the entrance time of this part of the T7 DNA increases in the case of the T7 mutant D111 (which contains a deletion of the A2 and A3 promoters) and decreases in the case of the D53 mutant (which contains a deletion in the region of the early gene transcription terminator). It would appear, that the second stage of the phage DNA transport is tightly coupled with its transcription and that a mechanical function is carried out by RNA polymerase. The translation inhibitors completely block the entrance of the remaining 40 per cent of the 17 DNA molecule (class III genes) into the host cell. It would appear that some class I and (or) II gene product(s) are obligatory components of the final stage of 17 DNA transport. Some probable consequences of this virus DNA transport model as well as its agreement with the functional structure of T7 chromosome and with T7 development are discussed.

On some aspects in stochastic dynamic programming with terminal region

A stochastic control problem with terminal region is considered making use of Markov controlled model. The familiar framework of the problem is as follows. Let the terminating time 7 of control process be defined as the first entrance time into the terminal region T and required to be finite with probability 1. The expectation of a cost functional which evaluates the system behavior until 7, is usually minimized with respect to the admissible control law somehow defined. Since the terminating time is of stochastic nature, the problem may be considered to have infinite horizon. Roughly speaking, this paper is concerned with two subjects associated with the approach of stochastic dynamic programming. Supposing that the state space does not include any topology, one of them is to provide a sufficient condition for measurability of the optimum cost function, which will be defined pointwise, and to show that under the same condition optimality equation is fulfilled everywhere in the state space. Another subject is originated from the question about computability of the optimum cost function and existence of optimal control law. This question relates closely to the uniqueness property of the optimality equation. In connection with this point, let the control problem be generalized so that the control process may be permitted to continue infinitely, while a newly introduced cost x(x1 9 x2 Y.) is imposed on this infiniteness. Of course the problem reduces to the original one when x = co. Dynamic programming approach then yields the same necessary condition for the optimum cost functions g, under a natural assumption for x, which means that the optimality equation need not have a unique solution. The circumstances may well illustrate the difficulty of finding the optimum cost function desired. In accordance with the state of affairs, the optimum cost functions g, are studied as a generalized version of the problem. The organization of the paper is as follows. Section 2 prepares the mathematical preliminaries that are necessary in order to consider the infinite horizon case, and other descriptions of materials. The former subject is discussed in 638 0022-247X/78/0653-0638$02.00/0

The distribution of the maximum number of customers present simultaneously during a busy period for the queueing systems M/G/1 and G/M/1

The distribution of the maximum number of customers simultaneously present during a busy period is studied for the queueing systems M/G/1 and G/M/1. These distributions are obtained by using taboo probabilities. Some new relations for transition probabilities and entrance time distributions are derived.

The distribution of the maximum number of customers present simultaneously during a busy period for the queueing systems M/G/1 and G/M/1

The distribution of the maximum number of customers simultaneously present during a busy period is studied for the queueing systems M/G/1 and G/M/1. These distributions are obtained by using taboo probabilities. Some new relations for transition probabilities and entrance time distributions are derived.

The influence of the weight of the duodenal tube tip on its entrance time

1. A successful intubation of the duodenum was accomplished in a two-hour period with any one of four tubes used, in about 90% of the attempts. 2. A lead weighted tip appears to hasten entrance into the duodenum. This, however, has not been determined beyond doubt. 3. Increasing the weight of the tip from 69 grains (Twiss Tube) to 150 grains (Moses Einhorn Tube 1938) does not appear to accelerate its passage, or increase the percentage of successes.